Question Number 1812 by 112358 last updated on 04/Oct/15 $${Find}\:{the}\:{period}\:{of}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)={cos}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\right)+{sin}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}−\frac{\pi}{\mathrm{4}}\right). \\ $$$${How}\:{may}\:{one}\:{find}\:{the}\:{period} \\ $$$${of}\:{the}\:{following}\:{functions} \\ $$$${if}\:\psi\left({x}\right)\:{has}\:{period}\:{m}\:{and}\:\gamma\left({x}\right) \\ $$$${has}\:{period}\:{n}? \\ $$$$\left(\mathrm{1}\right)\:{f}_{\mathrm{1}} \left({x}\right)=\psi\left({x}\right)\gamma\left({x}\right) \\ $$$$\left(\mathrm{2}\right)\:{f}_{\mathrm{2}}…
find-the-series-solution-of-the-ordinary-differential-equation-y-2-2xy-1-3y-x-2-1-y-0-1-and-y-1-0-2-
Question Number 132881 by Engr_Jidda last updated on 17/Feb/21 $${find}\:{the}\:{series}\:{solution}\:{of} \\ $$$${the}\:{ordinary}\:{differential}\:{equation} \\ $$$${y}^{\mathrm{2}} +\mathrm{2}{xy}^{\mathrm{1}} −\mathrm{3}{y}={x}^{\mathrm{2}} −\mathrm{1} \\ $$$${y}\left(\mathrm{0}\right)=\mathrm{1}\:{and}\:{y}^{\mathrm{1}} \left(\mathrm{0}\right)=\mathrm{2} \\ $$ Terms of Service…
Question Number 132880 by faysal last updated on 17/Feb/21 $${cot}\left(\mathrm{142}.\mathrm{5}°\right)=? \\ $$ Commented by bramlexs22 last updated on 17/Feb/21 $$\mathrm{285}°=\:\mathrm{2}×\mathrm{142}.\mathrm{5} \\ $$$$\mathrm{285}°=\mathrm{270}°+\mathrm{15}° \\ $$$$\mathrm{cot}\:\mathrm{285}°\:=\:\mathrm{cot}\:\mathrm{285}° \\…
Question Number 1809 by alib last updated on 04/Oct/15 $$\mathrm{tan}\:{a}+\mathrm{cot}\:{a}+\mathrm{tan}\:\mathrm{3}{a}+\mathrm{cot}\:\mathrm{3}{a}=\frac{\mathrm{8cos}\:^{\mathrm{2}} \mathrm{2}{a}}{\mathrm{sin}\:\mathrm{6}{a}} \\ $$$$ \\ $$ Commented by alib last updated on 04/Oct/15 $$\boldsymbol{{prove}} \\ $$…
Question Number 67345 by Aditya789 last updated on 26/Aug/19 $$\mathrm{3}{sinx}+\mathrm{5}{cosx}=\mathrm{5}\:{then}\:{prove}\:{that}\: \\ $$$$\mathrm{5}{sinx}−\mathrm{3}{cox}=\:+\mathrm{3} \\ $$ Answered by $@ty@m123 last updated on 26/Aug/19 $$\frac{\mathrm{3}}{\mathrm{5}}\mathrm{sin}\:{x}+\mathrm{cos}\:{x}=\mathrm{1} \\ $$$$\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}=\frac{\mathrm{3}}{\mathrm{5}} \\…
Question Number 1808 by alib last updated on 04/Oct/15 $$\boldsymbol{\mathcal{P}}{rove}\:\:\mathrm{sin}\:\left({a}\right)+\mathrm{sin}\:\left({a}+\frac{\mathrm{14}\pi}{\mathrm{3}}\right)+\mathrm{sin}\:\left({a}−\frac{\mathrm{8}\pi}{\mathrm{3}}\right)=\mathrm{0}/ \\ $$$$ \\ $$ Answered by 112358 last updated on 05/Oct/15 $${Using}\:{the}\:{compound}\:{angle}\:{formula} \\ $$$${sin}\left({x}\pm{y}\right)={sinxcosy}\pm{cosxsiny}\:{we}\:{get} \\…
Question Number 132877 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….\:{nice}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}\:: \\ $$$$\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right).{log}^{\mathrm{2}} \left({x}\right)}{{x}} \\ $$$$\:\:\:\:\:\:\:=\frac{\pi}{\mathrm{24}}\left(\mathrm{12}\gamma^{\:\mathrm{2}} +\pi^{\mathrm{2}} \right)\:….. \\ $$ Answered by…
Question Number 67342 by mathmax by abdo last updated on 26/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{\infty} \:\:\:\frac{{sin}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} −{x}\:+\mathrm{3}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 132876 by mnjuly1970 last updated on 17/Feb/21 Commented by Dwaipayan Shikari last updated on 17/Feb/21 $$\phi'\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:\:\phi\left({x}\right){is}\:{defined}\:{in}\:{Q}\mathrm{132877} \\ $$ Terms of Service Privacy Policy…
Question Number 1805 by ình Plus 001 last updated on 03/Oct/15 $${WTF} \\ $$ Answered by 123456 last updated on 03/Oct/15 $$\mathrm{Dolphins} \\ $$$$ \\…